A325710 Number of maximal subsets of {1..n} containing no products of distinct elements.

1, 1, 2, 2, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 24, 28, 32, 32, 62, 62, 92, 102, 184, 184, 254, 254, 474, 506, 686, 686, 1172, 1172, 1792, 1906, 3568, 3794, 5326, 5326, 10282, 10618, 14822, 14822, 25564, 25564, 35304, 39432, 76888, 76888, 100574, 100574, 197870, 201622, 282014

Offset: 0

Author

Gus Wiseman, Jul 09 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(9) = 6 maximal subsets:
  {1}  {1}  {1}   {1}    {1}     {1}     {1}      {1}       {1}
       {2}  {23}  {234}  {2345}  {2345}  {23457}  {23457}   {234579}
                                 {2456}  {24567}  {23578}   {235789}
                                 {3456}  {34567}  {24567}   {245679}
                                                  {25678}   {256789}
                                                  {345678}  {3456789}
		

Links

• Andrew Howroyd, PARI Program

Crossrefs

Subsets without products of distinct elements are A326117.

Maximal product-free subsets are A326496.

Subsets with products are A326076.

Maximal subsets without sums of distinct elements are A326498.

Maximal subsets without quotients are A326492.

Maximal subsets without sums or products of distinct elements are A326025.

Cf. A121269, A151897, A326116, A326489, A326497, A326024.

Programs

Mathematica

fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Times@@@Subsets[#,{2,n}]]=={}&]]],{n,0,10}]

PARI

\\ See link for program file.
for(n=0, 30, print1(A325710(n), ", ")) \\ Andrew Howroyd, Aug 29 2019

Extensions

Terms a(16) and beyond from Andrew Howroyd, Aug 29 2019